Given g(x)=(3x+5)2

Question

, which of the following shows that creating the equation of the inverse means switching the variables and solving for y?(1 point)
Responses

y=(3x−5)2
y equals Start Fraction left parenthesis 3 x minus 5 right parenthesis over 2 End Fraction

y=13(2x−5)
y equals Start Fraction 1 over 3 End Fraction left parenthesis 2 x minus 5 right parenthesis

y=(2x+5)3
y equals Start Fraction left parenthesis 2 x plus 5 right parenthesis over 3 End Fraction

y=23(x−5)

Answer 1

To find the inverse of the function \( g(x) = (3x + 5)^2 \), we need to switch the variables \( x \) and \( y \) and then solve for \( y \).

1. Start with \( y = (3x + 5)^2 \).
2. Switch \( x \) and \( y \): \( x = (3y + 5)^2 \).
3. Solve for \( y \).

The correct response from the provided choices should reflect this process.

To analyze the options:

1. y = (3x − 5)^2: This doesn't match our inverse function.
2. y = 1/3 (2x − 5): This also doesn't match our inverse.
3. y = (2x + 5)^3: This isn't the inverse as per our steps.
4. y = 2/3 (x − 5): This option doesn't match the expected steps.

None of the options provided appear to correctly illustrate the inverse of \( g(x) = (3x + 5)^2 \).

To actually derive the inverse correctly would yield a more complicated expression, which is not presented in the choices. The actual steps include taking the square root and rearranging terms, which doesn't correlate directly with any of the given options.

In conclusion, the options provided do not represent the proper switching of variables and the process of solving for \( y \).